The distance between two objects can be calculated using the Friis transmission equation. In its simplest form, the Friis transmission equation provides for the determination of power received by a receive antenna under idealized conditions given a transmit antenna some distance away transmitting at known amount of power. More specifically, the Friis transmission equation recites:
      P    r    =            G      t        ⁢                                        G            r                    ⁡                      (                          λ                              4                ⁢                                                                  ⁢                π                ⁢                                                                  ⁢                R                                      )                          2            ·              P        t            
Where,                R is the range or distance between the transmit antenna and the receive antenna;        Gt is the transmitter antenna(s) gain;        Gr is the receiver antenna(s) gain;        Pt is the power at which a signal is transmitted by a radiating object;        Pr is the power at which the signal is received by the radiating object; and        λ is the wavelength of the operating frequency.        
Consequently, by knowing the transmitted and received power, antenna gain values, and the wavelength, the unknown range R (or distance) between the transmit antenna and the receive antenna can be determined using the Friis transmission equation. The Friis transmission equation assumes operation in free space with the absence of any multipath. Multipath is the propagation phenomenon that results in radio signals reaching the receiving antenna by two or more paths. The effects of multipath include constructive and destructive interference, and phase shifting of the signal. In other words, a single path of energy flow between the transmitter and the receiver in free space will be replaced with multiple paths of energy flow caused by reflections from the objects and surfaces existing in the environment. Causes of multipath can include atmospheric ducting, ionospheric reflection and refraction, and reflection from water bodies and terrestrial objects such as mountains and buildings.
As a real time application, it is very beneficial to efficiently calculate the distance between an array and a wireless receiver (e.g. “client or receiver”) in wireless power delivery environment. Unfortunately, wireless power delivery environments (e.g., home, office, retail, etc.) often include multipath as walls and other Radio Frequency (RF) reflective objects affect and/or otherwise obstruct direct line of sight between the transmitting and receiving objects.
Accordingly, a need exists for technology that overcomes the problem demonstrated above, as well as one that provides additional benefits. The examples provided herein of some prior or related systems and their associated limitations are intended to be illustrative and not exclusive. Other limitations of existing or prior systems will become apparent to those of skill in the art upon reading the following Detailed Description.